A representation theorem for end spaces of infinite graphs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912007124418560 |
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| author | Kurkofka, Jan Pitz, Max |
| author_facet | Kurkofka, Jan Pitz, Max |
| contents | End-spaces of infinite graphs naturally generalise the Freudenthal boundary and sit at the interface between graph theory, geometric group theory and topology.
Our main result is that every end-space can topologically be represented by a special order tree. Our main proof ingredient is a structure theorem that we introduce, which carves out the order-tree-like structure of any graph in such a way that there is a natural bijection between the ends of the graph and the limit-type down-closed chains of the order-tree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_12670 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A representation theorem for end spaces of infinite graphs Kurkofka, Jan Pitz, Max Combinatorics 05C63, 06A07 End-spaces of infinite graphs naturally generalise the Freudenthal boundary and sit at the interface between graph theory, geometric group theory and topology. Our main result is that every end-space can topologically be represented by a special order tree. Our main proof ingredient is a structure theorem that we introduce, which carves out the order-tree-like structure of any graph in such a way that there is a natural bijection between the ends of the graph and the limit-type down-closed chains of the order-tree. |
| title | A representation theorem for end spaces of infinite graphs |
| topic | Combinatorics 05C63, 06A07 |
| url | https://arxiv.org/abs/2111.12670 |